I believe my heater core is either clogged or its gone bad. I have a 92 acura legend.

My heater doesn't blow any hot air at all or any air period. Im also losing coolant very fast. Can my heater core be the reason as to why I'm losing coolant so fast? There isn't any coolant leaking into my passenger side carpet, there's just the smell of coolant inside my car. Can it be my water pump or a weak radiator cap?

Could be leaking only when driving, could be leaking into your oil. Check
your oil and make sure there is no coolant in it and check your coolant
and make sure there is no oil in it. Bottom line is that you are leaking
coolant and when your coolant is low, you lose your heat. Find the leak.
If you can't find the leak yourself, take the vehicle to a mechanic and they
will run a simple pressure test and will find your leak fast.